Frequency Relationships of Air Pollution: a Case Study for PM2.5
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International Journal of Environmental Research and Public Health Article Establishment of Regional Concentration–Duration– Frequency Relationships of Air Pollution: A Case Study for PM2.5 Hone-Jay Chu * and Muhammad Zeeshan Ali Department of Geomatics, National Cheng Kung University, Tainan 70101, Taiwan; [email protected] * Correspondence: [email protected] Received: 5 February 2020; Accepted: 19 February 2020; Published: 22 February 2020 Abstract: Poor air quality usually leads to PM2.5 warnings and affects human health. The impact of frequency and duration of extreme air quality has received considerable attention. The extreme concentration of air pollution is related to its duration and annual frequency of occurrence known as concentration–duration–frequency (CDF) relationships. However, the CDF formulas are empirical equations representing the relationship between the maximum concentration as a dependent variable and other parameters of interest, i.e., duration and annual frequency of occurrence. As a basis for deducing the extreme CDF relationship of PM2.5, the function assumes that the extreme concentration is related to the duration and frequency. In addition, the spatial pattern estimation of extreme PM2.5 is identified. The regional CDF identifies the regional extreme concentration with a specified duration and return period. The spatial pattern of extreme air pollution over 8 h duration shows the hotspots of air quality in the central and southwestern areas. Central and southwestern Taiwan is at high risk of exposure to air pollution. Use of the regional CDF analysis is highly recommended for efficient design of air quality management and control. Keywords: PM2.5; duration; frequency; spatial map 1. Introduction Air pollution has become a worldwide environmental health risk [1,2], especially in the developing countries. In management, an essential task is to understand the duration, frequency, and intensity of air pollution [3,4]. Poor air quality usually affects human health [5–7]. Elderly people, children, and people with heart or lung conditions are more sensitive than others to the effects of inhaling fine particles (PM2.5). Acute exposure to PM2.5 is associated with various health outcomes, such as respiratory symptoms [8,9], hospital admissions, or death [10]. The maximum PM2.5 concentrations have significant positive impacts on outpatient visits [11]. Chronic exposure to PM2.5 can lead to chronic diseases or reduced life expectancy [12]. The risk that extreme pollutant concentrations pose to human health is the subject of environmental concern [10]. The impact of frequency and duration of air quality has received considerable attention over the past decades. However, few people discuss the concentration–duration–frequency (CDF) relationships in air pollution. The CDF is modified from the intensity–duration–frequency (IDF) relationship, which is a mathematical relationship between the rainfall intensity, duration, and annual frequency of occurrence [13]. The most common IDF techniques from hydrological engineering were used for Gumbel distribution [14]. However, the CDF is related to the extreme concentration of air pollution with its duration and annual frequency of occurrence. The CDF formulas are empirical equations representing a relationship between the maximum concentration as a dependent variable and other parameters of interest, i.e., duration and annual frequency of occurrence. In the frequency aspect, the Int. J. Environ. Res. Public Health 2020, 17, 1419; doi:10.3390/ijerph17041419 www.mdpi.com/journal/ijerph Int. J. Environ. Res. Public Health 2020, 17, 1419 2 of 13 return period of an event might be 100 years and is expressed as its probability of occurring being 1/100, or 1% in any one year. Many types of distributions, such as log-normal, Weibull, Pearson, gamma, and Gumbel distributions, are used to fit the distribution of air pollutant concentration [10,15–18]. The probability of occurrence and the CDF of extreme PM2.5 can be investigated using standard statistical techniques, e.g., Gumbel, log-normal, and Weibull probability distributions. In this study, the CDF analysis of fine aerosols was performed using the Gumbel probability distribution. The analysis system uses the actual measurement records to calculate the occurrence values of different frequencies according to the statistical properties of the samples and presumes the possible devaluation values to derive the basis of the extreme CDF relationship. Moreover, the empirical CDF relationship in this study is assumed to be the Bernard formula function [13,19]. The coefficient estimation is performed in a regression, and the estimated extreme concentration based on the defined return period and duration is finally obtained. The CDF analysis for a single station can be derived from historical data of PM2.5. However, the spatial pattern of air pollution is heterogeneous [20]. The regional CDF function is developed and determined on the basis of the regional parameters. Based on interpolation, the regional parameters can be estimated. The regional CDF analysis provides spatial patterns of extreme air pollution and further provides detailed spatial patterns in areas where no observations are available. The model estimates the extreme concentrations at unknown locations by simultaneously considering the regional parameters and using the regional CDF function as proxy information to provide information on the relationships of spatial patterns of air quality with various durations and return periods. Using the regional CDF analysis, the hotspot area of air pollution with a specified duration and return period can be identified. The objective of the study was to develop the relationship between the extreme PM2.5 concentration, the duration, and the frequency of occurrence. As a basis for deducing the Gumbel extreme value distribution and the empirical CDF model, the extreme concentration was assumed to be related to the duration and frequency, and the coefficient estimation was carried out in a regression. Furthermore, regional CDF estimations were conducted. It was expected that the regional CDF would identify the regional extreme concentration map with a specified duration and return period. 2. Materials and Study Area Figure1 shows the locations of air quality monitoring stations in Taiwan. Air quality zones, e.g., northern, central, southwestern, and eastern, are also established in Taiwan (Figure1). The Taiwanese Environmental Protection Agency (TWEPA) has been regularly recording the air quality and meteorological data throughout Taiwan since July 1982 [20]. Since August 2005, the TWEPA has completed the installation of 76 monitoring instruments for fine airborne aerosols (PM2.5; Figure1). In this study, the historical data obtained by the TWEPA’s Air Monitoring Network were obtained for the PM2.5 hourly fine aerosol concentration in Taiwan from 2005 to 2015. This study used the hourly PM2.5 obtained by the TWEPA stations that are in compliance with the regulatory air monitoring procedures. Int. J. Environ. Res. Public Health 2020, 17, 1419 3 of 13 Int. J. Environ. Res. Public Health 2020, 17, x FOR PEER REVIEW 3 of 13 FigureFigure 1.1. LocationsLocations ofof PMPM2.52.5 monitoringmonitoring stations stations.. 3.3. Method Methodss First,First, the moving average ofof PM2.52.5 datadata for for various various durations durations need neededed to be prepared. Derivations of the PM2.5 CCDFDF relationships relationships for for each each station station for for the different different return periodsperiods were determined by fittingfitting the Gumbel distribution to the correspondingcorresponding maximum concentration per year at various stations (Section(Section 3.13.1)).. The empirical model for thethe PMPM2.52.5 CDFCDF analysis at each station was developed (Section(Section 3.23.2)).. Eventually, thethe regionalregional PMPM2.52.5 CDF analysis w wasas performed ( (SectionSection 3.3)3.3).. 3.1. Derivations of PM2.5 CDF 3.1. Derivations of PM2.5 CDF The probability of occurrence of the extreme pollution event (C c) for the annual frequency of The probability of occurrence of the extreme pollution event (퐶≥≥ 푐) for the annual frequency F exceedanceof exceedance ( ) ( is퐹) the is the inverse inverse of theof the return return period period calculated calculated as follows:as follows: 11 P푃((C퐶 ≥c푐))==F퐹== (1(1)) ≥ T푇 The probability ofof non-exceedancenon-exceedance isis asas follows:follows: 1 푃(퐶 ≤ 푐) = 1 −1 (2) P(C c) = 1 푇 (2) ≤ − T where 푇 is the return period or recurrence interval of extreme concentration, 퐶 is the extreme PM2.5 whereconcentrationT is the, returnand 푐 is period the threshold or recurrence. interval of extreme concentration, C is the extreme PM2.5 concentration,The Gumbel distribution and c is the was threshold. fitted to the extreme PM2.5 data, i.e., to the maximum annual values. The cumulative Gumbel extreme value distribution is illustrated as follows [21]: −α(퐶−β) 푃(퐶 ≤ 푐) = 푒−푒 (3) Int. J. Environ. Res. Public Health 2020, 17, 1419 4 of 13 The Gumbel distribution was fitted to the extreme PM2.5 data, i.e., to the maximum annual values. The cumulative Gumbel extreme value distribution is illustrated as follows [21]: e α(C β) P(C c) = e− − − (3) ≤ where P(C c) is the probability of non-exceedance, and α and β are the parameters of the Gumbel ≤ distribution. From the observed sequence, the parameters can be estimated [13]. The parameters α and β are linked to the mean value (C) of the extreme PM2.5 data and to the standard deviation (σC) of the extreme PM2.5 data through the following equations: 1.282 α = (4) σC 0.577σ β = C C = C 0.45σ (5) − 1.282 − C The logarithm was taken twice to yield a formulation from Equation (3), and Equation (2) was merged into Equation (3). Thus, the extreme concentration of PM2.5 (C) for each return period is as follows: 1 C = β ln(lnT ln(T 1)) (6) − α − − In addition, C can be expressed as a function of the return period for each duration. The average extreme concentrations for various durations were calculated based on the aforementioned steps.